結果

問題 No.74 貯金箱の退屈
ユーザー ecotteaecottea
提出日時 2023-06-23 16:24:05
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 37 ms / 5,000 ms
コード長 10,107 bytes
コンパイル時間 4,306 ms
コンパイル使用メモリ 257,336 KB
最終ジャッジ日時 2025-02-15 00:32:06
ジャッジサーバーID
(参考情報)
judge4 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 30
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;
double EPS = 1e-15;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define YES(b) {cout << ((b) ? "YES\n" : "NO\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
//using mint = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
//
/*
*
*
* Bit_matrix<M>(int n, int m) : O(n M / 64)
* n×m
* m ≦ M
*
* Bit_matrix<M>(int n) : O(n M / 64)
* n×n
*
* Bit_matrix<M>(vector<bitset<M>> a, int m) : O(n M / 64)
* a[0..n)[0..m)
*
* Bit_matrix<M>(vi[vl] a, int m) : O(n M / 64)
* a[i] j v[i][j]
*
* push_back(bitset<M> col) : O(M / 64)
* col
*
* A * x : O(n M / 64)
* n×m A m x
*
* A * B : O(n m l)
* n×m A m×l B
*
* Bit_matrix<M> pow(ll d) : O(n^3 log d)
* d
*
* Bit_matrix<M> transpose() : O(n m)
*
* n ≦ M
*/
template <int M>
struct Bit_matrix {
int n, m; // n m
vector<bitset<M>> v; //
// n×m
Bit_matrix(int n, int m) : n(n), m(m), v(m) {}
// n×n
Bit_matrix(int n) : n(n), m(n), v(n) { rep(i, n) v[i][i] = 1; }
// a[0..n)[0..m)
Bit_matrix(const vector<bitset<M>>& a, int m) : n(sz(a)), m(m), v(a) {}
// a[i] j v[i][j]
Bit_matrix(const vi& a, int m) : n(sz(a)), m(m), v(n) { rep(i, n) v[i] = bitset<M>(a[i]); }
Bit_matrix(const vl& a, int m) : n(sz(a)), m(m), v(n) { rep(i, n) v[i] = bitset<M>(a[i]); }
Bit_matrix() : m(0), n(0) {}
//
Bit_matrix(const Bit_matrix& old) = default;
Bit_matrix& operator=(const Bit_matrix& other) = default;
//
bool operator==(const Bit_matrix& g) const { return n == g.n && m == g.m && v == g.v; }
bool operator!=(const Bit_matrix& g) const { return !(*this == g); }
//
inline bitset<M> const& operator[](int i) const { return v[i]; }
inline bitset<M>& operator[](int i) { return v[i]; }
//
void push_back(const bitset<M>& col) { v.push_back(col); n++; }
//
bitset<M> operator*(const bitset<M>& x) const {
bitset<M> y;
rep(i, n) y[i] = (v[i] & x).count() % 2;
return y;
}
//
Bit_matrix operator*(const Bit_matrix& b) const {
Bit_matrix res(n, b.m);
rep(i, res.n) rep(j, res.m) rep(k, m) res[i][j] = res[i][j] ^ (v[i][k] & b[k][j]);
return res;
}
Bit_matrix& operator*=(const Bit_matrix& b) { *this = *this * b; return *this; }
//
Bit_matrix pow(ll d) const {
Bit_matrix res(n), pow2 = *this;
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
// A^T
Bit_matrix transpose() const {
Bit_matrix res(m, n);
rep(i, m) rep(j, n) res[i][j] = v[j][i];
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Bit_matrix& a) {
rep(i, a.n) {
os << "[";
rep(j, a.m) os << a[i][j] << (j < a.m - 1 ? " " : "]");
if (i < a.n - 1) os << "\n";
}
return os;
}
#endif
};
//O(n m min(n, m) / 64)
/*
* n×m A n b
* A x = b x0m false
*
* gauss_jordan_elimination<N> gcc
*/
template <int M>
bool gauss_jordan_elimination(const Bit_matrix<M>& A, const vb& b, bitset<M>* x0) {
int n = A.n, m = A.m;
// v : (A | b)
vector<bitset<M + 1>> v(n);
rep(i, n) rep(j, m) v[i][j] = A[i][j];
rep(i, n) v[i][m] = b[i];
// pivots[i] : i
vi pivots;
//
int pi = -1, pj = -1;
// v[i][j]
int i = 0, j = 0;
while (i < n && j <= m) {
// 1
int i2 = i;
while (i2 < n && v[i2][j] == 0) i2++;
//
if (i2 == n) {
j++;
continue;
}
// i
pi = i; pj = j;
if (i != i2) swap(v[i], v[i2]);
// v[i][j]
pivots.push_back(j);
// i j 0 i XOR
rep(i2, n) if (v[i2][j] && i2 != i) v[i2] ^= v[i];
//
i++; j++;
}
// m
if (pivots.back() == m) return false;
//
if (x0 != nullptr) {
x0->reset();
int rnk = sz(pivots);
rep(i, rnk) (*x0)[pivots[i]] = v[i][m];
}
return true;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n;
cin >> n;
vi d(n), w(n);
cin >> d >> w;
Bit_matrix<100> A(n, n);
rep(i, n) {
int l = smod(i - d[i], n);
int r = smod(i + d[i], n);
A[l][i] = 1;
A[r][i] = 1;
}
dump(A);
vb b(n);
rep(i, n) b[i] = 1 - w[i];
dump(b);
bitset<100> x0;
bool res = gauss_jordan_elimination<100>(A, b, &x0);
dump(x0);
Yes(res);
}
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